In addition, we aim to evaluate the impact of the single-reflection and double-reflection channel components on the performance of the proposed integrated IRS-BS architecture. Towards this end, we define two benchmark channel setups for performance comparison, where only the single-reflection channel components, i.e., \(\mbox{{$ f $}}_{k,j}^{n_j},~k\in \mathcal {K},j\in \mathcal {J},n_j\in \mathcal {N}_j\) , are considered (termed as “single-reflection only”), and only the double-reflection channel components, i.e., \(\mbox{{$ g $}}_{k,j,q}^{n_j,n_q},~k\in \mathcal {K}, j\ne q\in \mathcal {J},n_j\in \mathcal {N}_j, n_q\in \mathcal {N}_{q}\) , are considered (termed as “double-reflection only”), respectively. Our proposed channel setup in (REF ) is termed as “single- and double- reflection”. We also consider the conventional multi-antenna BS without integrated IRS as a benchmark scheme, which is termed as “no-IRS”. For all setups employing IRSs, we adopt Algorithm REF  to design the reflection coefficients of all IRSs by assuming that perfect CSI is available at the BS. Besides, we aim to study the impact of the total number of reflecting elements \(N\)  on the performance of all schemes with integrated IRSs. Thus, we increase \(N_{j,1}\)  from 1 to 5 and fix \(N_{j,2}=8,~j\in \mathcal {J}\) , and thus the total number of reflecting elements \(N\)  is increased from 32 to 160.To reduce the computational complexity, we apply the IRS element grouping strategy [1]}, [2]} when \(N\ge 32\)  to group the reflecting elements in the same \(y\) -axis of each IRS into a subsurface, which will employ a common reflection coefficient. Under this strategy, the total number of subsurfaces under all considered \(N\)  values is fixed as \(\tilde{N}=32\) .
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